LOG114_12 Datasheet, PDF (21/29 Pages) Burr-Brown (TI) – Single-Supply, High-Speed, Precision LOGARITHMIC AMPLIFIER

LOG114
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INSIDE THE LOG114
The LOG114 uses two matched logarithmic amplifiers
(A₁ and A₂ with logging diodes in the feedback loops) to
generate the outputs log (I₁) and log (I₂), respectively.
The gain of 6.25 differential amplifier (A₃) subtracts the
output of A₂ from the output of A₁, resulting in [log (I₁)
− log (I₂)], or log (I₁/I₂). The symmetrical design of the
A₁ and A₂ logarithmic amps allows I₁ and I₂ to be used
interchangeably, and provides good bandwidth and
phase characteristics with frequency.
DEFINITION OF TERMS
Transfer Function
The ideal transfer function of the LOG114 is:
ǒ Ǔ V_LOGOUT + 0.375
log
I₁
1₂
(17)
This transfer function can be seen graphically in the typ-
ical characteristic curve, V_LOGOUT vs I_REF.
When a pedestal, or offset, voltage (V_Com) is connected
to the Com pin, an additional offset term is introduced
into the equation:
ǒ Ǔ V_LOGOUT + 0.375
log ^I1
1₂
) V_Com
(18)
Accuracy
Accuracy considerations for a log ratio amplifier are
somewhat more complicated than for other amplifiers.
This complexity exists because the transfer function is
nonlinear and has two inputs, each of which can vary
over
a
wide
dynamic range. The accuracy for any combination of
inputs is determined from the total error specification.
Total Error
The total error is the deviation of the actual output from
the ideal output. Thus,
V_{LOGOUT(ACTUAL)} = V_{LOGOUT(IDEAL)} ± Total Error
It represents the sum of all the individual components
of error normally associated with the log amp when op-
erating in the current input mode. The worst-case error
for any given ratio of I₁/I₂ is the largest of the two errors
when I₁ and I₂ are considered separately. Temperature
can also affect total error.
Errors RTO and RTI
As with any transfer function, errors generated by the
function may be Referred-to-Output (RTO) or Referred-
to-Input (RTI). In this respect, log amps have a unique
property: given some error voltage at the log amp out-
put, that error corresponds to a constant percent of the
input, regardless of the actual input level.
SBOS301A − MAY 2004 − REVISED MARCH 2007
Log Conformity
For the LOG114, log conformity is calculated in the
same way as linearity and is plotted as I₁/I₂ on a semi-
log scale. In many applications, log conformity is the
most important specification. This condition is true be-
cause bias current errors are negligible (5pA for the
LOG114), and the scale factor and offset errors may be
trimmed to zero or removed by system calibration.
These factors leave log conformity as the major source
of error.
Log conformity is defined as the peak deviation from the
best fit straight line of the V_LOGOUT versus log (I₁/I₂)
curve. Log conformity is then expressed as a percent of
ideal full−scale output. Thus, the nonlinearity error ex-
pressed in volts over m decades is:
V_{LOGOUT (NONLIN)} = 0.375V/decade • 2Nm
where N is the log conformity error, in percent.
INDIVIDUAL ERROR COMPONENTS
The ideal transfer function with current input is:
V_{LOGOUT IDEAL} + 0.375
ǒ Ǔ log I1
1₂
(19)
The actual transfer function with the major components
of error is:
ǒ Ǔ 0.375(1 " DK)
log ^I1
I₂
" 2Nm " V_OSO
(20)
where:
∆K = gain error (0.4%, typ, as specified in the Electri-
cal Characteristics table)
I_B1 = bias current of A₁ (5pA, typ)
I_B2 = bias current of A₂ (5pA, typ)
m = number of decades over which the log
conformity error is specified
N = log conformity error (0.1%, typ for m = 5 decades;
0.9% typ for m = 7.5 decades)
V_OSO = output offset voltage (11mV, typ for ±5V sup-
plies; 14mV, typ for +5V supplies)
To determine the typical error resulting from these error
components, first compute the ideal output. Then calcu-
late the output again, this time including the individual
error components. Then determine the error in percent
using Equation (21):
%error
+
Ť_{V LOGOUT}
*V _IDEAL
LOGOUT
Ť
TYP
V _LOGOUTIDEAL
100%
(21)
21